Linear Relationship between the Dielectric Constant and Band Gap in Low-Dimensional Mixed-Halide Perovskites

Inorganic halide perovskites CsPbX3 (X = Cl, Br, I) with excellent thermal stability are widely drawing increasing attention from researchers in light-emitting diodes and solar cells. The band gap and dielectric constant are two important parameters to characterize the optoelectronic performance in semiconductors. To map the underlying relationship between the dielectric constant and band gap for mixed-halide perovskites, atomic and electronic properties including mixing enthalpy, band gap, and dielectric constant in different halogen concentrations, substitution sites, and dimensions are investigated systematically using density functional theory. The results demonstrate that both dimensionality and halide composition have a small influence on mixing enthalpy, and structures with different halogen concentrations are prone to form at room temperature in bulk and monolayer perovskites. The increase in the band bowing parameter is 0.004-0.196 eV in the case of tuning the composition, while the increased value is 0.440-0.549 eV by increasing the dimensionality from monolayer to bulk counterpart, suggesting that the method of controlling dimensions has more influence on their band bowing than halide composition. Furthermore, we obtained an apparent positive linear correlation between the dielectric constant and 1/E-g(2), which can be useful to deeply understand the dielectric properties of all dimensionalities. Our work provides a theoretical basis for different dimensionality and composition perovskite materials with potential applications in optoelectronic devices.